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Nonlinear mechanics of a compliant beam system undergoing large curvature deformation

Akano Theddeus Tochukwu, Olayiwola Patrick Shola

Archive of Mechanical Engineering

2020

LXVII, nr 4

471--489

A compliant beam subjected to large deformation is governed by a multifaceted nonlinear differential equation. In the context of theoretical mechanics, solution for such equations plays an important role. Since it is hard to find closed-form solutions for this nonlinear problem and attempt at direct solution results in linearising the model. This paper investigates the aforementioned problem via the multi-step differential transformation method (MsDTM), which is well-known approximate analytical solutions. The nonlinear governing equation is established based on a large radius of curvature that gives rise to curvature-moment nonlinearity. Based on established boundary conditions, solutions are sort to address the free vibration and static response of the deforming flexible beam. The geometrically linear and nonlinear theory approaches are related. The efficacy of the MsDTM is verified by a couple of physically related parameters for this investigation. The findings demonstrate that this approach is highly efficient and easy to determine the solution of such problems. In new engineering subjects, it is forecast that MsDTM will find wide use.

Vibration analysis of single-walled carbon nanotubes conveying nanoflow embedded in a viscoelastic medium using modified nonlocal beam model

Hosseini M., Sadeghi-Goughari M., Atashipour S. A., Eftekhari M.

Archives of Mechanics

2014

Vol. 66, nr 4

217--244

In this study, the vibration and stability analysis of a single-walled carbon nanotube (SWCNT) coveying nanoflow embedded in biological soft tissue are performed. The effects of nano-size of both fluid flow and nanotube are considered, simultaneously. Nonlocal beam model is used to investigate flow-induced vibration of the SWCNT while the small-size effects on the flow field are formulated through a Knudsen number (Kn), as a discriminant parameter. Pursuant to the viscoelastic behavior of biological soft tissues, the SWCNT is assumed to be embedded in a Kelvin–Voigt foundation. Hamilton’s principle is applied to the energy expressions to obtain the higher-order governing differential equations of motion and the corresponding higher-order boundary conditions. The differential transformation method (DTM) is employed to solve the differential equations of motion. The effects of main parameters including Kn, nonlocal parameter and mechanical behaviors of the surrounding biological medium on the vibrational properties of the SWCNT are examined.